Math Problem Statement
Correct?
Solution
The steps shown in your image are essentially correct, but let's break it down and analyze the details.
You start with the expression: This represents the absolute value, which can be interpreted as the distance between and on a number line.
Steps Explanation:
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Expression : This is interpreted as the absolute distance between and . So, the original expression is correct in describing the "distance between and 3."
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Factoring out : The next step is factoring out the from inside the absolute value expression: This is mathematically sound because pulling out a negative factor doesn’t change the overall value inside the absolute value. The absolute value function ignores signs.
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Simplification : You remove the because: So this is also correct. The absolute value of a negative or positive expression is the same as that of the original expression.
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Conclusion: The expression represents the distance between and 3.
Final Verdict:
Your steps are correct, and the final result shows that is equivalent to , as both represent the same distance.
Do you want details on how absolute values represent distances or any clarifications? Here are five questions to help expand your understanding:
- What is the geometric interpretation of absolute value on a number line?
- How does factoring affect expressions inside an absolute value?
- Why is true for any number ?
- Can we generalize the property that for any linear function ?
- What happens if we add or subtract constants from absolute value expressions?
Tip: Remember, the absolute value of any real number is its distance from 0, regardless of direction on the number line!
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value
Factoring
Formulas
|a| = distance between a and 0
|a - b| = distance between a and b
Theorems
Absolute Value Property
Distance Formula
Suitable Grade Level
Grades 7-10